AMD Ryzen 1600X:-3.6 GHz @ 6 Cores, 12 Threads, Turbo 4 GHz, 16MB Cache, 65W TDP
Pros:-
) A great alternative for better workflow than the I5.
) One of the best game and live streaming line up currently in the market.
) More cores - the 1600x has 2 more cores, 8 more threads and double the amount of cache the 7600k has.
) As all of the Zen processors are unlocked, so you can gain extra 100-200 MHz by overclocking through BIOS or the AMD Ryzen Master program. The lower TDP gives Ryzen even further room for overclocking.*

Cons:-
) Lower clockspeed means it's not going to be that great at gamnig.
) Less RAMs and cooling soltuins are compatible with the Ryzen family as of now, compared to Intel's Kaby Lake family.
) No integrated graphics in the chip.

Cons:-
) Lower core count, so it falls back compared to Ryzen when it comes to productivity(video editing, 3D sculpturing etc)
) Not as great at live streaming as Ryzen is.
) Higher TDP.

Personally I'd recommend going for AMD Ryzen 1600X if you are in a budget while wanting to own a computer that is capable of doing somewhat heavy workload, like video editing or live streaming. Otherwise, if you game a lot without doing workloads or multitasking that often, then go for the 6600K, 6700K or even the 7600K - 6600K is a better value chip out of the three, but it is your choice.
I built my newest computer with a Ryzen 1700 chip as it offered a great bang for the buck, and it is a 8 cores 16 threads monster so it makes me capable of doing a bunch of things in Blender and video editing in After Effects and having them minimized while playing GTA V with no problem at all.

* = Make sure to have a better cooling solution, like water, as these chips can run hot.

Personally I'd recommend going for AMD Ryzen 1600X if you are in a budget while wanting to own a computer that is capable of doing somewhat heavy workload, like video editing or live streaming. Otherwise, if you game a lot without doing workloads or multitasking that often, then go for the 6600K, 6700K or even the 7600K - 6600K is a better value chip out of the three, but it is your choice.
I built my newest computer with a Ryzen 1700 chip as it offered a great bang for the buck, and it is a 8 cores 16 threads monster so it makes me capable of doing a bunch of things in Blender and video editing in After Effects and having them minimized while playing GTA V with no problem at all.

* = Make sure to have a better cooling solution, like water, as these chips can run hot.

The best part about owning a Ryzen chip is the ability to upgrade on the line - the AM4 socket supports all* Zen processors up to Ryzen 7 1800X.
Due to the high demand of the cheaper Ryzen chips on the market, like the Ryzen 3 and Ryzen 5, you can easily sell your used 1600/1600X on a nearby store or on eBay, and with a bit more, you can get a 1700. The Ryzen 7 1700 is comparable to an I7 6950X; a chip that costs $1,000 more than the 1700, yet only delivers about 35% more performance...not really a great investment for a chip that only has two more cores and a higher turbo speed than the 1700(a diminishing return).
Here, watch a few videos that includes thoughts from the bigger tech YouTubers about the newest chips, including benchmarks.

tl;dr: Buy any Ryzen chip and you can upgrade up to 1800X later in the future. For productivity, the I7 6950X offers 35% more performance than the Ryzen 7 1700 but it costs $1,000 more.
* = Threadripper has the socket TR4 instead of AM4 so it is not compatible with AM4 boards.